17 



between trough and crest. The surface curve cuts the level y=0 



(equation 136) at 



L—a. J 3i+o 

 x= — -. — and x= — -. — 

 4 4 



Rewriting equation 14a in terms of h and substituting from equa- 

 tion 12a, for (7, the rate of drift or mass transport at a distance z 

 below the surface is given as: 



^£2 



'-yjl^z (146) (9) 



Here, z is negative when measured downward from the surface. 



VELOCITY DISTRIBUTION OF MASS TRANSPORT 

 IN A CLOSED CHANNEL 



NOTE: 

 AREA AOB EQUALS AREA BCD. 

 ORIGIN O REFERS TO OBSERVED 

 VELOCITIES WHILE O' APPLIES 

 TO EQUATION 12 



Figure 6. 



Integi'ating this equation between and — co ^ we obtain as the total 

 volume transfer per unit width of wave crest 



G=h'J 



gTr_ 

 32i 



(14c) 



The average velocity of drift down to some depth d (which must exceed 

 i/2 if the theory is to apply) is 





32L 



(14^0 



Ua is approximately the magnitude of the undertow or return flow 

 along the bottom which must exist in a channel closed at the end 

 toward which the waves travel. The observed velocity distribution 

 would be as shown in figure 6. 



If the waves are set up m a closed tank, the velocity distribution 

 in equation 146 must be compensated for a reverse motion which 



